The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Answer:
Step-by-step explanation:
First confirm that x = 1 is one of the zeros.
f(1) = 2(1)^3 - 14(1)^2 + 38(1) - 26
f(1) = 2 - 14 + 38 - 26
f(1) = -12 + 38 = + 26
f(1) = 26 - 26
f(1) = 0
=========================
next perform a long division
x -1 || 2x^3 - 14x^2 + 38x - 26 || 2x^2 - 12x + 26
2x^3 - 2x^2
===========
-12x^2 + 28x
-12x^2 +12x
==========
26x -26
26x - 26
========
0
Now you can factor 2x^2 - 12x + 26
2(x^2 - 6x + 13)
The discriminate of the quadratic is negative. (36 - 4*1*13) = - 16
So you are going to get a complex result.
x = -(-6) +/- sqrt(-16)
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2
x = 3 +/- 2i
f(x) = 2*(x - 1)*(x - 3 + 2i)*(x - 3 - 2i)
The zeros are
1
3 +/- 2i
Answer:
x=10/3 y=17/3
Step-by-step explanation:
Use substitution to solve your equation. Plug in y=2x-1 into y=1/2x+4. This makes (2x-1)=1/2x+4. Simplify this to get 3/2x-1=4. Simplify it again to get 3/2x=5. No one likes fractions so multiply both sides by 2 to get 3x=10. Simplify this and get x=10/3. Plus 10/3 into one of the equations. You can pick anyone but I picked y=2x-1. Because you know x=10/3, you put y=2(10/3)-1. Simplify this and get y=20/3-1. Convert 1 into a fraction and get y=20/3-3/3. Simplify this and get y=17/3.
Therefore,
x=10/3 y=17/3
Hoped this helps you
Answer:
almost 3 per minute but not just about there yet
Step-by-step explanation:
34/12 = 2.8333333333~
Answer:
Step-by-step explanation:
- We first compute the ratio of this geometric sequence.
- We simplify the fractions:
- We deduce that it is the common ratio because it is the same between each pair.
- We use the first term and the common ratio to describe the equation:
<h3>We apply the data in this formula:</h3>
_______________________
<h3>We apply:</h3>
<u>Data</u>: The unknown "n" is the term you want
<h3><em><u>MissSpanish</u></em></h3>
